Apparatus for drafting and measuring angles.



No. 831,314. PATENTED SEPT.18, 1906.

W. J. VARLEY.

APPARATUS FOR DRAFTING AND MEASURING ANGLES.

APPLIGATION FILED APR. 6. 1906.

2 SHEETSSHBBT 1.

rm: mmms PETERS Cw. nmsuuvmoy. u. c.

No. 831,314; I PATENTED SEPT. 18, 1906.

W. J. VARLEY.

.APPARATUS FOR DRAFTING AND MEASURING ANGLES.

APPLIOAIION TIL E1) APR. 6. 1906.

2 SHEETS-SHEET 2.;-

HWHIIWHUII for Drafting and Measuring UNITED STATES PATENT OFFICE.

APPARATUS FOR DRAFTING AND MEASURING ANGLES.

Y No. 831,314.

Application filed April 6, 1906. Serial No To all whont it may concern:I

Be it known that I, WILLIAM J. VARLEY, a citizen of the United States,residing at Englewood, in the county of Bergen and State of New Jersey,have invented certain new and useful Improvements in Apparatus Angles,of which the following is a full, clear, and exact description.

My invention relates to the art of drafting and measuring, and pertainsparticularly to the provision of an instrument used in these arts andthe method in the performance of which the instrument is convenientlyused.

The principal object of the invention is to enable draftsmen andengineers. to perform operations on the drawing-board which havehitherto been altogether impossible, or only possible by the aid oftrigonometrical tables, protractors, and other machinery with which theaverage draftsman is ordinarily unsupplied and with the use of which heis not particularly familiar.

A further object of the invention is to enable results to be determinedwith absolute accuracy, or as nearly absolute accuracy as graphicalmethods can attain, in place of approximate results, which depend onmathematical tables and constants.

' With these and other objects in view my invention consists in themethods and in the construction and arrangements, as hereinafter setforth and shown and finally par ticularly pointed out in the appendedclaims.

In the drawings, Figure 1 is a diagrammatic view illustrating theformation of what I shall term an arcuate rectification curve, and whichembodies the essential principles of my invention. Fig. 2 is a diagramillustrating the curve and some of its properties. Fig. 3 is a similarview designed to show still further properties. Fig. 4 shows a draftingimplement embodying the curve above mentioned. Fig. 5 shows another formof drafting implement also making use of the curve.

In modern engineering a wide variety of mathematical operations areperformed by raphical methods directly upon the drawingoard. T-squaresand steel straight-edges are now brought to such perfection thathorizontal and vertical lines are obtainable with great accuracy, aswell as forty-five-degree an sixty-degree lines, circles, and arcs ofcircles. With these a wide variety of problems can be solved; but so faras I am aware a certain class of problems have fallen out of the rangeSpecification of Letters Patent.

' very troublesome,

each other in a vertical line passing Patented Sept. 18, 1906.

of utility of drafting methods hitherto used and have had to be solvedby the aid of mathematical tables and constants. Foremost of suchproblems are those relating to laying off or measurement of specialangles. Protractors with verniers are sold for doing this; but theinstrument is an expensive and delicate one and out of place whenexposed to the rough usage of the ordinary drafting-board. On thisaccount it is more usual for draftsmen to lay off special angles bynatural sign or tangent tables, which of course is a round aboutoperation and somewhat liable to error. In carrying out my invention Ipro vide an instrument which is as cheap and simple as the ordinarydraftsmans triangles and which is capable of measuring off arcs andangles of any value and with absolute accuracy.

In addition to the laying off or measurement of angles problemsfrequently arise involving the measurement of sectors and the areas ofsegments. These are ordinarily and my invention pro vides a graphicalmethod of obtaining the desired results with absolute accuracy or withas much accuracy as drafting implements can attain.

A further object of the invention is to divide a circle into any numberof parts with the same facility as is possible in the subdivision of astraight line.

In order that my invention may be fully understood, I will state theessential principles which I have discovered, and of which I make useand embody in the structure or instrument later described.

Referring to the drawings, in which like parts are designated by thesame reference sign wherever they occur, Fig. 1 shows a diagrammaticgeneration of the arcuate rectification curve. In this figure, Adesignates a roller or wheel revoluble on a fixed axis 0, and Crepresents a rod having a straight-edge D, which bears against theperiphery of the wheel A and is constrained to have a rectilinear orright-line movement on the line (1 d. E indicates a pointer fixedlyattached to the wheel A, so as to turn therewith, and F indicates astraight-edge fixedly attached to the as to rectilinearly movetherewith. Now sup osing the straight-edges E andF are initia lyarranged, so as to coincide with through the axis 0, and then themembers C and A or idealized apparatus for the are moved or rolled inthe direction of the arrows, the intersection of the straight-edges Eand F will describe a curve G, which somewhat resembles a parabola ingeneral form, passing through an originat the point 0 and approaching apair of parallel asymptotes h and i. The essential characteristic of thecurve G is that any point therein is the same linear distance from theline 0 0 as the arc subtended by such point on the periphery of thewheel A. Expressed in other words, the curve G is the locus of a rightline having a uniform rectilinear motion and of another right linehaving a uniform angular motion about a fixed point. It is evident thatthe angle E 0 0 is always proportional to the distance of theintersecting point in the curve from the line 0 0. If this distance isw, it may be stated that w=K d, where 6 is the angle E 0 0. Anotherexpression for the curve is y =00 cot (9, where y is the distance of thepoint on the curve from a horizontal line passing through -0. Thisequation, therefore, is based on rectangular coordinates whose origin is0. The angle 6 may be expressed in terms of 00, since 0: where 1' is theradius of the wheel A. The

equation therefore becomes y=0c cot I consider the form in which theequation is expressed as, however, relatively unimportant, since it.would be expressed in different ways for the varying systems ofcoordinates used. In all cases, however, its essential characteristic isillustrated by the diagram of Fig. 1, the essential characteristic beingthat every point on the curve intersects every radius of a certain areat the same distance from a base-line as the length of the arc. Thebase-line in Fig. 1 is the line 0 0, and the arc is of course thecircumference of the wheel A. The arcuate rectification curve beingobtained by the above or any other method, it may be embodied in variousways and used for various now describe. In Fig. 2 the curve is shown atG, the base-line at 0 0, and the arc at a. 0 1" is a radial line. Such aradius cuts the are a at the point r and the curve G at the point 1'. Ifa perpendicular r s is erected at the point r, the distance 0 s will bee ual to the arc 0 r. This gives a ready met 0d of laying off andmeasuring angles. For ex ample, supposing it were desired to lay off anangle of 36.47 from the line 0 0, the curve G being drawn from abase-circle a of any radius, it is merely necessary to lay off thedistance 0 s proportional to the angle wanted. In the present case theline 0 8 would be 36. 47 units long. The perpendicular s 1" beingdropped to cut the curve G, the angle 0 0 1* is formed, which is theangle 36.47

purposes, which I will required. If the base-circle a, is taken of theright radius, it is obvious that the units used in measuring off theline 0 8 may be inches or centimeters or any other unit which isobtainable on the scales sold upon the market. In practice I make theradius of the circle at equal to or 5.729578 inches, as by this figurethe distance 0 8 may be measured off as 3.647 inches in order to get theangle mentioned. The measurement of any unknown angle is effected by thesimple reversal of the above process. In ordinary practice the curve Gwould of course be drawn with an instrument having a fixed contour oredge to guide the pencil, and the various horizontals and perpendicularswould be made by the T-square and triangles. It is this fact thatrenders the method useful and practical for draftsmen and others whodesire to secureaccurate results quickly and easily.

In Fig. 3 I have reproduced the essential parts of the diagram of Fig. 2in order to illustrate another field of utility of my inventionnamely,to measure the areas of sectors and segments. Supposing it is desired toobtain the area of the sector 0 0 r. The point 8 is obtained, as before,by erectin a perpendicular from the point 1" and a racIial line 0 s isdrawn. Then the area of the triangle 0 0 s is equal to the area of thesector This follows since the line 0 s is equal to the arc 0 1". Thusthe draftsman obtains at once a triangle of area equal to the sector. Ifit is desired to measure the area of the segment 0 r, a secondperpendicular is erected from the point r to the point 8. Then the areaof the segment is equal to that of the triangle o s s. This follows fromthe fact that the segment equals the area of the Sector minus the areaof the triangle 0 o 1" equals the triangle 0 o 8 minus the triangle 0' 07" equals the triangle 0 r 8. When itis desired to divide a circle intoany number of parts, it is merely necessary to lay off the anglecorresponding to any chosen number of parts by linear measure on theline 0 s and subdivide this measure into the chosen number of parts.Radial lines from the point 0 through the intersection of perpendicularsfrom the divisions on the line 0 s with the curve G then cut the circleinto the number of divisions required. The number of applications of myinvention is practically unlimited; but the above will serve asillustrative examples and will sufficiently indicate the field ofutility thereof.

Referring now to Figs. 4 and 5, I illustrate one form of practicalconstruction which embodies my invention. This comprises a plate 1, ofsheet metal, having straight edges 2 and 3 at right angles to oneanother and having a curved'edge 4, which corresponds exproperly dividethe circle.

actly to the curve G above described, and l which I term the arcuaterectification curve. The edges 2 and 3 are respectively parallel to thediagrammatic lines 0 and 0 s above described. 5 indicates a hole whichis accurately situated in the plate 1 at the point 0 of the abovediagrammatic representation. The plate 1 is conveniently cut away at 6and 7 so as to lighten the construction; but a web 8 may be left forgreater strength and for the attachment of a handle 9. The deviceillustrated in Fig. 4 may be termed a right-hand instrument. A left-handinstrument would be similar, except that all of the parts would betransposed from right to left. If the knob 9 were omitted, theinstrument shown would serve equally well as a right or as a left handinstrument by merely turning it upside down.

In Fig. 5 another form of tool is shown which embodies a differentportion of the curve. The portion of the curve is denoted by G andcomprises a section extending equal distances from either side of thepoint 0 in the diagrams previously described 10 designates a hole whichcan be registered with a line corresponding to the line 0 0. The edge 11is straight and corresponds with a horizontal line intersecting thecircle a at a fortyfive degree radius thereof. This instrument isparticularly convenient for the sub division of circles, since it ismerely necessary to register the edge 11 with the four sides of asuitable square and then after having divided the square into a suitablenumber of divisions to draw perpendiculars therefrom intersecting thevarious curves G. Radial lines through the intersecting points will thenWhat I claim is 1. A drafting implement comprising a plate or sheet ofmaterial having one edge curved in accordance with the equation y =w cotand having means whereby the coordinates of the curve may be located.

2. A drafting implement comprising a plate or sheet of material havingtwo straightedges at right angles to one another, and a' third edgecurved in accordance with the gr; equation y=0c cot and having meanswhereby the coordinates of the curve may be located.

3. A drafting implement comprising a plate or sheet of material having apair of straight-edges at right angles to one another and having a thirdedge curved in accordance with the equation y=zr cot i, said platehaving a hole centered at the origin ofthe coordinates of said curve,and having means whereby the coordinates of the curve may be located.

. 4. A drafting implement having one curved edge any point of which isthe same distance from the diameter of a base-circle as the length ofthe arc subtended by a radius through such point, and having meanswhereby the coordinates of the curve may be located.

In witness whereof I subscribe my signature in the presence of twowitnesses.

WILLIAM J. VARLEY. Witnesses:

FRANK S. OBER, ALFRED W. PRocToR.

